Plenary and Semi-Plenary Lectures
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| Title: |
| Discontinuous Galerkin Method and Its Applications |
| Lecturer: |
| Chi-Wang Shu |
| Abstract: |
| Discontinuous Galerkin method is a finite element method which resembles a finite volume method using numerical fluxes and having a local conservation property. It was first designed for solving first order hyperbolic conservation laws, however in recent years it has been generalized to solve convection dominated convection diffusion equations such as the Navier-Stokes equations and partial differential equations containing even higher order spatial derivatives such as the KdV equations. The discontinuous Galerkin method has been gaining popularity quite rapidly over the past few years, as it has nice stability properties for a wide class of linear and nonlinear problems, is flexible for h-p adaptivity, and has excellent parallel efficiency. In this talk we will first survey the general methodology of the discontinuous Galerkin method. We will then describe a few recent developments of the method and its applications, including stable and convergent local discontinuous Galerkin method for a wide class of nonlinear dispersive wave equations, kinetic-hydrodynamic multiscale problems by domain decomposition using the discontinuous Galerkin method in gas dynamics and device simulations, and discontinuous Galerkin methods based on non-polynomials building blocks. |
 Chi-Wang Shu is a professor of Applied Mathematics at Brown University. His research interest is in numerical solutions for partial differential equations, especially non-oscillatory high order numerical methods for convection dominated partial differential equations. He has worked on total variation bounded methods, total variation diminishing high order Runge-Kutta time discretizations, essentially non-oscillatory (ENO) and weighted ENO (WENO) finite difference and finite volume methods, discontinuous Galerkin methods, and spectral methods for discontinuous problems, with applications in computational fluid dynamics, semiconductor device simulations, traffic flow problems, astrophysics, biology, and other areas. He received his B.Sc. degree in mathematics from the University of Science and Technology of China in 1982 and his Ph.D. degree in mathematics from UCLA in 1986. He is the managing editor of the American Mathematical Society journal Mathematics of Computation, the co-chief editor of the Journal of Scientific Computing, and he serves in the editorial boards of 11 other journals. He is an ISI Highly Cited Author in Mathematics by ISI Web of Knowledge, and received the first Feng Kang Prize of Scientific Computing in 1995. |
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